It has been known for many years to practice seismic exploration of the earth. For example, according to the "Vibroseis" method currently popular, acoustic energy is imparted to the earth at a first location. It will be understood that the term "acoustic" when used here and in the discussion that follows should be construed to include all possible types of wave propagation in the earth. The acoustic wave thus generated passes downwardly through the earth and is reflected from interfaces between rock layers of varying density to be retransmitted upwardly towards the surface of the earth. It is detected by a plurality of detectors, which are termed "geophones" when an exploration is performed on the surface of the earth or "hydrophones" when it is performed on the ocean. The present invention relates to both modes; use of the term "geophone" should therefore be construed to include "hydrophones", and so on, as indicated by the context. The records output by the geophones are typically analog waveforms showing relatively high amplitude peaks where the reflected burst is received by the detector. If a plurality of such records are corrected for the differing source-to-receiver distance and are printed side by side, the peaks will line up. This can be taken as an indication of the presence of an interface between rock layers. These pictures can then be used by the geophysicist in the location of subterranean formations likely to contain oil, gas or other valuable minerals. See, e.g., U.S. Pat. No. 3,611,278 to Guinzy and Ruehle.
It will be appreciated that in addition to true primary reflection events, the time of detection of which is indicative of the depth of an interface beneath the surface, events of less easily interpreted physical significance, e.g., after multiple reflections have taken place at rock layer interfaces, also occur. Accordingly, it is possible for a seismic record to be ambiguous or to be misinterpreted. Therefore, where this possibility is deemed to be present, it is known to derive a synthetic seismogram using ray tracing modeling techniques. The path of a wave comparable to that actually input to the earth is traced through a hypothesized subterranean structure in accordance with known laws of reflection and refraction such as Snell's law. In general the incident angle of the wave with respect to the earth's surface is varied and plural rays traced. The outputs of the arbitrarily selected input paths may then be interpolated to yield a synthetic seismogram comparable to a real seismogram, i.e., one having inputs determined by the physical location of geophones with respect to the source, which can then be compared with the real seismogram; the degree to which the synthetic seismogram matches the real is thus an indication of the accuracy of the model used.
As noted above, the typical ray tracing programs used in the prior art to generate synthetic seismograms for comparison with real seismograms to measure the accuracy of a model hypothesized generally require selection of downward-going ray paths in a first layer as the beginning of the ray tracing program. The ray traced eventually emerges from the earth some distance from the source. Since in real exploration practices, the output waves are detected at locations determined by the physical location of geophones with respect to the source, it is necessary to interpolate the output points of the rays traced to correspond to the positions of the actual geophones before the seismograms can be directly compared. Not only is this interpolation process costly of computer time but it is also possible that the interpolated results may not be valid. For example, it has been discovered that the output of a geophone does not vary simply as a function of the distance between the source and the receiver (the "offset"). Therefore, the use of interpolation as a means of generalizing specific output results to hypothetical geophone locations can lead to serious inaccuracies in the synthetic seismogram thus generated. U.S. Pat. No. 3,671,929 to Ruehle et al is an example of such a modeling process, in which initial angles of ray travel are specified, and the results interpolated to correspond to an actual seismogram; U.S. Pat. No. 3,651,451 to Ruehle described a method of estimating the velocity of an acoustic wave in a subterranean layer useful in the generation of such synthetic seismograms.